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This didn't get through on the first post...
-------- Original Message --------
Subject: Painting by numbers: Fractal art produces pictures worth 1,000
equations
Date: Sun, 31 Dec 2006 06:37:36 -0800
From: Roger Bagula <rlbagula@[EMAIL PROTECTED]
>
Newsgroups: sci.fractals,sci.nonlinear,alt.fractalks
( I recognize the author of the article : Scott La Fee has bee writing
for Copley News Service/ San Diego Union since the 1980's.)
http://www.bendweekly.com/news/1601.html
Dec 29,2006
Painting by numbers: Fractal art produces pictures worth 1,000 equations
by Scott LaFee
small font medium font large font
Fractals are like metaphysical Legos, building blocks that connect the
worlds of number and shape. But unlike the plastic toy bricks, you can't
see fractals, which are essentially algorithms or mathematical rules.
Instead, you see the patterns they produce, which are fundamentally
distinctive, to say the least.
All fractal patterns share a few common traits.
FRACTAL ART - “Warm Glow” is the product of a Mandelbrot set, perhaps
the most famous fractal. Coloration is based upon how many times each
pixel in the image was “visited” during repeating equations. CNS Photo
courtesy of Kerry Mitchell.
Each is self-similar. That is, the whole and the parts of the whole
share a resemblance, regardless of scale. This rule isn't always
obvious. Sometimes fractals can be self-similar only in a statistical
sense.
Each is recursive: the underlying math repeats again and again.
Each evokes a sense of nature. Indeed, nature abounds with examples of
fractals: branching rivers and blood vessels, swirling cloud systems,
the repeating patterns of mountain ranges and the rocks that comprise
them.
People have long looked at these patterns and been fascinated, but it
was not until the 1960s, when computers became sufficiently powerful,
that mathematicians, scientists and engineers began to create and
investigate fractals in their infinite detail.
It's been a fruitful endeavor. Fractal science allows researchers to
perceive order in apparent disorder. Fractal concepts have been used to
analyze the distribution of galaxies in the universe, the frequencies of
economic cycle indices and the probabilities of earthquakes and wildfires.
Along the way, fractals became art as well. Early efforts were colorful
but relatively crude: a psychedelic paisley of spikes, spirals and
zigzags. Today's art, like the math, has progressed. Powerful
off-the-shelf software programs can now create remarkably exquisite
fractal images on home computers.
Many employ a basic technique: Every pixel or point on the screen is
assigned a unique number. Each number is inserted into a mathematical
formula to produce a result. Each result is reinserted into the same
formula to produce a new result. This is done again and again, a process
called iteration. Pixels are then colored based on the mathematical
results, whether numbers got bigger or smaller.
The computer, of course, is critical. A small fractal image may contain
300,000 points, with each point processed through a fractal formula
1,000 times. That's 300 million calculations. A poster-sized image could
require 1 trillion calculations.
Massive number crunching doesn't guarantee a work of art. Indeed,
fractal calculations often produce more white noise than mathematical
masterpieces. That's where the artist comes in. To be successful, as
these examples from some of today's finest fractal practitioners show,
requires an understanding of both form and function.
Copley News Service
67 times read
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This didn't get through on the first post...<br>
<br>
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<table border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<th align="right" nowrap="nowrap" valign="baseline">Subject: </th>
<td>Painting by numbers: Fractal art produces pictures worth
1,000 equations</td>
</tr>
<tr>
<th align="right" nowrap="nowrap" valign="baseline">Date: </th>
<td>Sun, 31 Dec 2006 06:37:36 -0800</td>
</tr>
<tr>
<th align="right" nowrap="nowrap" valign="baseline">From: </th>
<td>Roger Bagula <a class="moz-txt-link-rfc2396E"
href="mailto:rlbagula@[EMAIL PROTECTED]
"><rlbagula@[EMAIL PROTECTED]
></td>
</tr>
<tr>
<th align="right" nowrap="nowrap" valign="baseline">Newsgroups:
</th>
<td>sci.fractals,sci.nonlinear,alt.fractalks</td>
</tr>
</tbody>
</table>
<br>
<br>
<pre>( I recognize the author of the article : Scott La Fee has bee
writing
for Copley News Service/ San Diego Union since the 1980's.)
<a class="moz-txt-link-freetext"
href="http://www.bendweekly.com/news/1601.html">http://www.bendweekly.com/news/1601.html</a>
Dec 29,2006
Painting by numbers: Fractal art produces pictures worth 1,000 equations
by Scott LaFee
small font medium font large font
Fractals are like metaphysical Legos, building blocks that connect the
worlds of number and shape. But unlike the plastic toy bricks, you can't
see fractals, which are essentially algorithms or mathematical rules.
Instead, you see the patterns they produce, which are fundamentally
distinctive, to say the least.
All fractal patterns share a few common traits.
FRACTAL ART - “Warm Glow” is the product of a Mandelbrot set, perhaps
the most famous fractal. Coloration is based upon how many times each
pixel in the image was “visited” during repeating equations. CNS Photo
courtesy of Kerry Mitchell.
Each is self-similar. That is, the whole and the parts of the whole
share a resemblance, regardless of scale. This rule isn't always
obvious. Sometimes fractals can be self-similar only in a statistical
sense.
Each is recursive: the underlying math repeats again and again.
Each evokes a sense of nature. Indeed, nature abounds with examples of
fractals: branching rivers and blood vessels, swirling cloud systems,
the repeating patterns of mountain ranges and the rocks that comprise
them.
People have long looked at these patterns and been fascinated, but it
was not until the 1960s, when computers became sufficiently powerful,
that mathematicians, scientists and engineers began to create and
investigate fractals in their infinite detail.
It's been a fruitful endeavor. Fractal science allows researchers to
perceive order in apparent disorder. Fractal concepts have been used to
analyze the distribution of galaxies in the universe, the frequencies of
economic cycle indices and the probabilities of earthquakes and wildfires.
Along the way, fractals became art as well. Early efforts were colorful
but relatively crude: a psychedelic paisley of spikes, spirals and
zigzags. Today's art, like the math, has progressed. Powerful
off-the-shelf software programs can now create remarkably exquisite
fractal images on home computers.
Many employ a basic technique: Every pixel or point on the screen is
assigned a unique number. Each number is inserted into a mathematical
formula to produce a result. Each result is reinserted into the same
formula to produce a new result. This is done again and again, a process
called iteration. Pixels are then colored based on the mathematical
results, whether numbers got bigger or smaller.
The computer, of course, is critical. A small fractal image may contain
300,000 points, with each point processed through a fractal formula
1,000 times. That's 300 million calculations. A poster-sized image could
require 1 trillion calculations.
Massive number crunching doesn't guarantee a work of art. Indeed,
fractal calculations often produce more white noise than mathematical
masterpieces. That's where the artist comes in. To be successful, as
these examples from some of today's finest fractal practitioners show,
requires an understanding of both form and function.
Copley News Service
67 times read
</pre>
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